A method for evaluating dynamic reliability of a bridge structure system

Abstract

The application discloses a bridge structure system dynamic reliability evaluation method and belongs to the technical field of bridge structure reliability evaluation. The method comprises the following steps: 1, determining the reliability calculation typical section according to the bridge structure characteristics and the monitoring system arrangement; 2, calculating the failure probability of each section of the bridge based on the deflection dynamic monitoring data; 3, calculating the failure probability of each section of the bridge based on the strain dynamic monitoring data; 4, bridge structure system dynamic reliability evaluation. The system reliability analysis of the application considers the multi-component cooperative failure path of the bridge as a redundant system, analyzes the overall failure probability, and the failure probability calculation problem of the bridge structure system can be attributed to the failure probability calculation problem of the series mode. The failure probability of the system is calculated by using the narrow boundary theory, the bridge structure system dynamic reliability is inversely calculated, the contradiction between the fitting precision and the generalization ability is reconciled, and the high-precision and dynamic reliability evaluation demand is met.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge structure reliability evaluation, and particularly relates to a bridge structure system dynamic reliability evaluation method. BACKGROUND

[0002] Bridge structure reliability refers to the probability that a bridge maintains a predetermined function (strength, stiffness, stability) under the action of environment and load within a predetermined service life. It is usually quantified by failure probability or reliability index. Reliability design needs to balance safety redundancy and construction cost to avoid overdesign or underdesign. As a core component of transportation infrastructure, the structural reliability of a bridge is directly related to public safety, economic operation, and social stability. The calculation method of bridge structure reliability has evolved from empirical safety factor to probability statistics and then to intelligent algorithm.

[0003] Traditional deterministic methods include safety factor method and allowable stress method. Safety factor method is an early design that relies on a fixed safety factor (such as a bending safety factor of 1.5). The safety of the structure is determined by comparing the ratio of the bearing capacity of the structure to the design load. This method is simple to calculate and suitable for early bridge design, but it does not consider the randomness of load and material properties, leading to conservative design or potential risks (such as fatigue failure of overloading bridges). Allowable stress method is to limit the maximum stress of the structure to be less than the allowable stress of the material, which is suitable for components such as steel bridges and concrete bridges that are mainly controlled by strength. However, it does not consider the statistical distribution of load and resistance, and cannot evaluate long-term performance degradation.

[0004] Probabilistic reliability theory methods include first-order second-moment method and Monte Carlo simulation method. First-order second-moment method is based on probability statistics theory, which evaluates the failure probability by solving the reliability index (value) of the performance function. It has high computational efficiency and is suitable for explicit performance function problems. However, it has poor applicability for nonlinear and implicit problems (such as material nonlinearity or complex boundary conditions). Monte Carlo simulation method is to approximate the true failure probability by a large number of random samples, which has high precision but extremely low computational efficiency, especially for large bridges that require tens of thousands of finite element analyses, making it difficult to apply in practice.

[0005] Modern reliability calculation methods mainly include surrogate modeling, system reliability analysis, and time-varying reliability analysis. Surrogate modeling uses machine learning algorithms to construct approximate models of function functions, replacing time-consuming high-precision finite element method (FEM) calculations, and reducing computational load by fitting implicit function functions. However, existing surrogate models suffer from a trade-off between fitting accuracy and generalization ability, and lack adaptability to high-dimensional parameter spaces. System reliability analysis considers the collaborative failure paths of multiple components in a bridge as a redundant system, analyzing the overall failure probability. Time-varying reliability analysis considers time-varying factors such as material corrosion and fatigue crack propagation, calculating the reliability degradation over time. With the increasing service life of bridges, the increasing complexity of environmental loads, and the surge in traffic volume, traditional reliability assessment methods are gradually revealing their limitations, failing to meet the demands for high-precision, dynamic reliability assessment. Therefore, a more accurate dynamic reliability assessment method is urgently needed. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for dynamic reliability assessment of bridge structural systems, addressing the shortcomings of the prior art.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for dynamic reliability assessment of bridge structural systems, characterized in that the method includes the following steps:

[0008] Step 1: Determine the typical cross-section for reliability calculation based on the bridge's structural characteristics and the layout of the monitoring system;

[0009] Step 2: Calculate the failure probability of each section of the bridge based on the dynamic deflection monitoring data. The process is as follows:

[0010] Step 201: Construct a deflection distribution model for each section of the bridge. The deflection of the main beam at the same section under moving load is proportional to the moving load. The moving load distribution model for each section of the bridge is the deflection distribution model for each section of the bridge.

[0011] Step 202: Fit the tail of the vehicle load data using a generalized Pareto distribution;

[0012] Step 203: Model all observation data exceeding the deflection threshold, and express the tail characteristics of the data distribution as follows: , Where N is the number of samples observed, and N is the number of samples exceeding the threshold. The scale parameter is the value beyond the quantity distribution. For shape parameters that exceed the quantity distribution, For observation data exceeding the deflection threshold, This is the deflection threshold;

[0013] Step 204: Determine the scale parameter of the excess quantity distribution. and shape parameters of the quantity distribution The value of is used to determine the probability distribution function of the extreme value of live load deflection. ,in, Let be the extreme value of the cross-sectional deflection, where For the remaining service life of the bridge, This represents the probability of exceeding the sample limit during the service life. , for The number of vehicle load effects exceeding the threshold within the time period; the remaining service life of the bridge. The expression is , For the design baseline period, For the design and use period, For the re-service period;

[0014] Step 205, according to the formula Calculate the first Probability of failure due to live load deflection of a bridge structural section , For the first The probability distribution function of the extreme values ​​of live load deflection of a bridge structural section For the first Theoretical limits of deflection for a single bridge structural section;

[0015] Step 3: Calculate the failure probability of each section of the bridge based on strain dynamic monitoring data. The process is as follows:

[0016] Step 301: Obtain the time-varying distribution of the axial resistance strength of concrete at each section of the bridge;

[0017] Step 302: Obtain the mean and standard deviation of the load effects at each section of the bridge;

[0018] Step 303, according to the formula Calculate the first Reliability index of bridge structural section ,in, For the first The average concrete resistance strength of each bridge structural section For the first Standard deviation of concrete resistance strength of each bridge structural section No. The mean value of the cross-sectional load response of each bridge structural section. For the first The standard deviation of the section load response of a bridge structural section;

[0019] Step 304, according to the formula Calculate the first Probability of strain failure of a bridge structural section ;in, This is the probability function of the standard normal distribution;

[0020] Step 4: Dynamic reliability assessment of the bridge structural system, the process is as follows:

[0021] Step 401: Determine the failure probability of each cross-section of the bridge structure under live load deflection. and the failure probability of strain at each section Sort the results from largest to smallest to obtain the failure probability sequence. , The first number of the failure probability data and , This represents the total number of failure probability data.

[0022] Step 402: Treat the bridge structure as a bridge structural system composed of typical cross-sections of each bridge connected in series. Transform the reliability calculation problem of the bridge structural system into a reliability calculation problem of a series system. Use narrow-bound theory to solve for the failure probability of this series system. ,in,

[0023]

[0024] The second number of the failure probability data and , This represents the probability of two failure modes failing simultaneously.

[0025] Step 403, according to the formula Calculate the dynamic reliability of the bridge structural system .

[0026] The above-mentioned method for dynamic reliability assessment of bridge structural systems is characterized in that: in step 203, the deflection threshold... The determination process is as follows:

[0027] Step 20301, according to the formula Calculate the sample mean , For the first One observation data point exceeding the deflection threshold. Choose 1, 2, ..., n;

[0028] Step 20302, according to the formula Calculate the sample kurtosis , The mean of samples exceeding the threshold;

[0029] Step 20303, if the sample kurtosis Elimination makes The largest value ;

[0030] Step 20304: Repeat steps 20301 to 20303 until... The maximum value in the data sample when the runtime stops. Deflection threshold .

[0031] The above-mentioned method for dynamic reliability assessment of bridge structural systems is characterized in that: in step 204, the scale parameter of the excess quantity distribution is determined. and shape parameters of the quantity distribution The process of obtaining the value is as follows:

[0032] Using the maximum likelihood estimation function Estimate the scale parameter of the quantity distribution. and shape parameters of the quantity distribution The value;

[0033] To each and Find the partial derivative and set it equal to 0. Shi De Solving this system of equations yields... and The maximum likelihood estimate.

[0034] The above-mentioned method for dynamic reliability assessment of bridge structural systems is characterized in that: in step 301, the axial resistance strength includes axial compressive strength or axial tensile strength, according to the formula... , obtain the Time-varying distribution of mean compressive strength of concrete in a bridge structural section and the Time-varying distribution of the standard deviation of the compressive strength of concrete in a bridge structural section ,in, For the first The initial value of the average compressive strength of concrete in each section of the bridge structure. is a time-varying factor for the mean compressive strength of concrete cubes. For the first The initial value of the standard deviation of the concrete compressive strength of each bridge structural section. is a time-varying factor for the standard deviation of the compressive strength of concrete cubes;

[0035] According to the formula , obtain the Time-varying distribution of mean tensile strength of concrete in a bridge structural section and the Time-varying distribution of the standard deviation of the tensile strength of concrete in a bridge structural section ,in, For the first The initial value of the average tensile strength of concrete in each section of the bridge structure. For the first The initial value of the standard deviation of the concrete tensile strength of each bridge structural section.

[0036] The above-mentioned method for dynamic reliability assessment of bridge structural systems is characterized in that: in step 302, according to the formula... +1.4 Calculate the first Mean value of cross-sectional load response of each bridge structural section ,in, For the first Mean value of dead load effect of each bridge structural section For the first The average stress of a bridge structural section under live load;

[0037] According to the formula +1.4 Calculate the first Standard deviation of the section load response of a bridge structural section ,in, For the first Standard deviation of dead load effect of each bridge structural section For the first The standard deviation of cross-sectional stress under live load on a bridge structure section.

[0038] The above-mentioned method for dynamic reliability assessment of bridge structural systems is characterized in that: in step 402, the probability of simultaneous failure of two failure modes is... ,in, , For monitoring data and monitoring data The correlation coefficient.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. This invention determines typical sections for reliability calculation based on the characteristics of bridge structures and the layout of monitoring systems. It collects the dynamic deflection of each typical section of the bridge and considers the randomness of vehicle load data. It models all observation data exceeding the deflection threshold, determines the values ​​of the scale parameter and shape parameter of the excess quantity distribution, and then determines the probability distribution of the extreme value of live load deflection. This enables the prediction of the failure probability of live load deflection at each typical section of the bridge structure without the need for tens of thousands of finite element analyses. It has good practical application results. The section reliability assessment based on actual bridge monitoring data provides a theoretical basis and technical support for the safety assessment of bridge structures and is easy to promote and use.

[0041] 2. This invention determines typical sections for reliability calculation based on the structural characteristics of the bridge and the layout of the monitoring system. It collects the dynamic strain of each typical section of the bridge, obtains the time-varying distribution of the axial resistance strength of the bridge concrete and the mean and standard deviation of the load effect of each section of the bridge. It uses the resistance strength and load effect data to obtain the reliability index of each typical section of the bridge and back-calculates the strain failure probability of each section of the bridge structure. This facilitates the combination with the probability distribution of the extreme value of live load deflection to obtain the failure probability of the bridge structure system. By considering the statistical distribution of load and resistance, it is convenient to evaluate the long-term performance degradation law.

[0042] 3. The method of this invention has simple steps. The system reliability analysis considers the collaborative failure path of multiple components of the bridge as a redundant system and analyzes the overall failure probability. The failure probability calculation problem of the bridge structure system can be reduced to the failure probability calculation problem of the series mode. The narrow-bound theory is used to calculate the failure probability of the system and back-calculate the reliability index of the bridge structure system. It reconciles the contradiction between fitting accuracy and generalization ability, meets the requirements of high-precision and dynamic reliability assessment, and is easy to promote and use.

[0043] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0045] like Figure 1 As shown, the present invention provides a method for dynamic reliability assessment of a bridge structural system, comprising the following steps:

[0046] Step 1: Determine the typical cross-section for reliability calculation based on the bridge's structural characteristics and the layout of the monitoring system;

[0047] Step 2: Calculate the failure probability of each section of the bridge based on the dynamic deflection monitoring data. The process is as follows:

[0048] Step 201: Construct a deflection distribution model for each section of the bridge. The deflection of the main beam at the same section under moving load is proportional to the moving load. The moving load distribution model for each section of the bridge is the deflection distribution model for each section of the bridge.

[0049] Step 202: Fit the tail of the vehicle load data using a generalized Pareto distribution;

[0050] Step 203: Model all observation data exceeding the deflection threshold, and express the tail characteristics of the data distribution as follows: , Where N is the number of samples observed, and N is the number of samples exceeding the threshold. The scale parameter is the value beyond the quantity distribution. For shape parameters that exceed the quantity distribution, For observation data exceeding the deflection threshold, This is the deflection threshold;

[0051] Step 204: Determine the scale parameter of the excess quantity distribution. and shape parameters of the quantity distribution The value of is used to determine the probability distribution function of the extreme value of live load deflection. ,in, Let be the extreme value of the cross-sectional deflection, where For the remaining service life of the bridge, This represents the probability of exceeding the sample limit during the service life. , for The number of vehicle load effects exceeding the threshold within the time period; the remaining service life of the bridge. The expression is , For the design baseline period, For the design and use period, For the re-service period;

[0052] Step 205, according to the formula Calculate the first Probability of failure due to live load deflection of a bridge structural section , For the first The probability distribution function of the extreme values ​​of live load deflection of a bridge structural section For the first Theoretical limits of deflection for a single bridge structural section;

[0053] Step 3: Calculate the failure probability of each section of the bridge based on strain dynamic monitoring data. The process is as follows:

[0054] Step 301: Obtain the time-varying distribution of the axial resistance strength of concrete at each section of the bridge;

[0055] Step 302: Obtain the mean and standard deviation of the load effects at each section of the bridge;

[0056] Step 303, according to the formula Calculate the first Reliability index of bridge structural section ,in, For the first The average concrete resistance strength of each bridge structural section For the first Standard deviation of concrete resistance strength of each bridge structural section No. The mean value of the cross-sectional load response of each bridge structural section. For the first The standard deviation of the section load response of a bridge structural section;

[0057] Step 304, according to the formula Calculate the first Probability of strain failure of a bridge structural section ;in, This is the probability function of the standard normal distribution;

[0058] Step 4: Dynamic reliability assessment of the bridge structural system, the process is as follows:

[0059] Step 401: Determine the failure probability of each cross-section of the bridge structure under live load deflection. and the failure probability of strain at each section Sort the results from largest to smallest to obtain the failure probability sequence. , The first number of the failure probability data and , This represents the total number of failure probability data.

[0060] Step 402: Treat the bridge structure as a bridge structural system composed of typical cross-sections of each bridge connected in series. Transform the reliability calculation problem of the bridge structural system into a reliability calculation problem of a series system. Use narrow-bound theory to solve for the failure probability of this series system. ,in,

[0061]

[0062] The second number of the failure probability data and , This represents the probability of two failure modes failing simultaneously.

[0063] Step 403, according to the formula Calculate the dynamic reliability of the bridge structural system .

[0064] In this embodiment, in step 203, the determination process of the deflection threshold value is as follows:

[0065] Step 20301, the sample mean value is calculated according to the formula , is the k-th observation data exceeding the deflection threshold value, k=1, 2, …, n;

[0066] Step 20302, the sample kurtosis is calculated according to the formula , is the sample mean value exceeding the threshold value;

[0067] Step 20303, if the sample kurtosis , the observation data that makes the maximum value is removed;

[0068] Step 20304, repeat steps 20301 to 20303 until , the maximum value in the data sample at the time of stopping running is the deflection threshold value .

[0069] In this embodiment, in step 204, the process of determining the values of the scale parameter of the excess distribution and the shape parameter of the excess distribution is as follows:

[0070] The maximum likelihood estimation function is used to estimate the values of the scale parameter of the excess distribution and the shape parameter of the excess distribution;

[0071] The partial derivatives of and are taken respectively, and they are equal to 0, when , the equation is obtained, and the maximum likelihood estimation values of and can be obtained by solving the equation group.

[0072] In this embodiment, in step 301, the axial core resistance strength includes axial core compression strength or axial core tensile strength, and the time-varying distribution of the mean value of the concrete body compression strength of the k-th bridge structure section is obtained according to the formula and the time-varying distribution of the mean value of the concrete body tensile strength of the k-th bridge structure section is obtained according to the formula .​Time-varying distribution of the standard deviation of the compressive strength of concrete in a bridge structural section ,in, For the first The initial value of the average compressive strength of concrete in each section of the bridge structure. is a time-varying factor for the mean compressive strength of concrete cubes. For the first The initial value of the standard deviation of the concrete compressive strength of each bridge structural section. is a time-varying factor for the standard deviation of the compressive strength of concrete cubes;

[0073] According to the formula , obtain the Time-varying distribution of mean tensile strength of concrete in a bridge structural section and the Time-varying distribution of the standard deviation of the tensile strength of concrete in a bridge structural section ,in, For the first The initial value of the average tensile strength of concrete in each section of the bridge structure. For the first The initial value of the standard deviation of the concrete tensile strength of each bridge structural section.

[0074] In this embodiment, in step 302, according to the formula +1.4 Calculate the first Mean value of cross-sectional load response of each bridge structural section ,in, For the first Mean value of dead load effect of each bridge structural section For the first The average stress of a bridge structural section under live load;

[0075] According to the formula +1.4 Calculate the first Standard deviation of the section load response of a bridge structural section ,in, For the first Standard deviation of dead load effect of each bridge structural section For the first The standard deviation of cross-sectional stress under live load on a bridge structure section.

[0076] In this embodiment, in step 402, the probability of both failure modes failing simultaneously is... ,in, , For monitoring data and monitoring data correlation coefficient.

[0077] In the implementation of the present application, according to the bridge structure characteristics and the monitoring system arrangement, the typical section for reliability calculation is determined, the dynamic deflection of each typical section of the bridge is collected, the randomness of the vehicle load data is considered, the modeling is performed on all observation data exceeding the deflection threshold, the scale parameter of the exceeding amount distribution and the value of the shape parameter of the exceeding amount distribution are determined, and then the probability distribution of the live load deflection extreme value is determined, so as to realize the live load deflection failure probability prediction of each typical section of the bridge structure, without using tens of thousands of times of finite element analysis, the actual application effect is good, the section reliability evaluation based on the real bridge monitoring data provides a theoretical basis and technical support for the safety evaluation of the bridge structure; according to the bridge structure characteristics and the monitoring system arrangement, the typical section for reliability calculation is determined, the dynamic strain of each typical section of the bridge is collected, the time-varying distribution of the axial force strength of the bridge concrete and the mean value and standard deviation of the load effect of each section of the bridge are obtained, the reliability index of each typical section of the bridge is obtained by using the axial force strength and load effect data, and the strain failure probability of each section of the bridge structure is inversely calculated, so as to facilitate the combination with the probability distribution of the live load deflection extreme value to obtain the failure probability of the bridge structure system, by considering the statistical distribution of the load and the resistance, the long-term performance degradation law is facilitated to be evaluated; the system reliability analysis is the multi-component cooperative failure path considering the bridge as a redundant system, the overall failure probability is analyzed, the failure probability calculation problem of the bridge structure system can be reduced to the failure probability calculation problem of the series mode, the failure probability of the system is calculated by using the narrow boundary theory, the reliability index of the bridge structure system is inversely calculated, the contradiction between the fitting precision and the generalization ability is reconciled, and the reliability evaluation demand of high precision and dynamic is met.

[0078] The above is only a preferred embodiment of the present application, and does not limit the present application in any way. Any simple modification, change and equivalent structure change of the above embodiment according to the technical essence of the present application are still within the protection scope of the technical solution of the present application.

Claims

1. A method for evaluating dynamic reliability of a bridge structure system, characterized by, The method comprises the following steps: Step one, according to the bridge structure characteristics and monitoring system arrangement to determine the reliability calculation typical section; Step two, based on the deflection dynamic monitoring data to calculate the failure probability of each section of the bridge, the process is as follows: Step 201, the deflection distribution model of each section of the bridge is constructed, the deflection of the same section of the main beam under the action of the moving load is proportional to the action of the moving load, and the moving load distribution model of each section of the bridge is the deflection distribution model of each section of the bridge; Step 202, the tail part of the vehicle load data is fitted by using the generalized Pareto distribution; Step 203, model all the observed data that exceeds the deflection threshold, the tail of the data distribution is characterized by a distribution expression , is the number of observed samples, N is the number of samples that exceed the threshold, is the scale parameter of the excess distribution, is the shape parameter of the excess distribution, is the observed data that exceeds the deflection threshold, is the deflection threshold; Step 204, determining the value of the scale parameter of the exceedance distribution and the shape parameter of the exceedance distribution , and further determining the probability distribution function of the live load deflection extreme value , wherein, is the cross-section deflection extreme value, wherein, is the remaining service life of the bridge, is the probability of the exceedance sample occurring within the service life, , is the number of vehicle load effects exceeding the threshold value collected within the time period; the remaining service life of the bridge is expressed as , is the design reference period, is the design service life, is the re-service life; Step 205, according to the formula Calculate the first Probability of failure due to live load deflection of a bridge structural section , For the first The probability distribution function of the extreme values ​​of live load deflection of a bridge structural section For the first Theoretical limits of deflection for a single bridge structural section; Step three, based on the strain dynamic monitoring data to calculate the failure probability of each section of the bridge, the process is as follows: Step 301, the time-varying distribution of the axial resistance strength of the concrete of each section of the bridge is obtained; Step 302, the mean value and standard deviation of the load effect of each section of the bridge are obtained; Step 303, according to the formula Calculate the first Reliability index of bridge structural section ,in, For the first The average concrete resistance strength of each bridge structural section For the first Standard deviation of concrete resistance strength of each bridge structural section No. The mean value of the cross-sectional load response of each bridge structural section. For the first The standard deviation of the section load response of a bridge structural section; Step 304, according to the formula Calculate the first Probability of strain failure of a bridge structural section ;in, The probability function is the standard normal distribution. Step four, the dynamic reliability evaluation of the bridge structure system, the process is as follows: Step 401, live load deflection failure probability of each section of the bridge structure and each section strain failure probability arrange from large to small, get failure probability sequence , the first number of failure probability data and , the total number of failure probability data; Step 402, the bridge structure is regarded as a bridge structure system connected by typical cross sections of each bridge, the reliability calculation problem of the bridge structure system is converted into a series system reliability calculation problem, and the failure probability of the series system is solved by using narrow bound theory wherein, is the second number for failure probability data and , is the probability of simultaneous failure of the two failure modes; Step 403, according to the formula Calculate the dynamic reliability of the bridge structural system .

2. The method for evaluating dynamic reliability of a bridge structure system according to claim 1, wherein: In step 203, the deflection threshold is determined as follows: Step 20301, calculate sample mean , according to the formula , is the th observation data exceeding the deflection threshold, take 1, 2,..., n; Step 20302, calculate the sample kurtosis , according to the formula , is the sample mean that exceeds the threshold value; Step 20303, if sample kurtosis , reject if numerically largest ; Step 20304, repeat steps 20301 to 20303 until the maximum value in the running data sample at the time of stopping is the deflection threshold .

3. The method for evaluating dynamic reliability of a bridge structure system according to claim 1, wherein: In step 204, the values of the scale parameter of the excess distribution and the shape parameter of the excess distribution are determined as follows: using a maximum likelihood estimation function to estimate values of a scale parameter of the excess distribution and a shape parameter of the excess distribution ; Take partial derivatives of and respectively, and set them equal to 0, when , we get Solving the equation set, we can get the maximum likelihood estimates of and .

4. The method for evaluating dynamic reliability of a bridge structure system according to claim 1, wherein: In step 301, the axial resistance strength includes axial compressive strength or axial tensile strength, according to the formula... , obtain the Time-varying distribution of mean compressive strength of concrete in a bridge structural section and the Time-varying distribution of the standard deviation of the compressive strength of concrete in a bridge structural section ,in, For the first The initial value of the average compressive strength of concrete in each section of the bridge structure. is a time-varying factor for the mean compressive strength of concrete cubes. For the first The initial value of the standard deviation of the concrete compressive strength of each bridge structural section. is a time-varying factor for the standard deviation of the compressive strength of concrete cubes; According to the formula , the time-varying distribution of the mean value of the tensile strength of the concrete body of the first bridge structure section and the time-varying distribution of the standard deviation of the tensile strength of the concrete body of the first bridge structure section are obtained, wherein is the initial value of the mean value of the tensile strength of the concrete of the first bridge structure section is the initial value of the standard deviation of the tensile strength of the concrete of the first bridge structure section.

5. The method for evaluating dynamic reliability of a bridge structure system according to claim 1, wherein: In step 302, the mean value of the cross-section load response of the i-th bridge structure cross-section is calculated according to the formula +1.4 , wherein, is the mean value of the cross-section dead load effect of the i-th bridge structure cross-section, is the mean value of the cross-section live load effect of the i-th bridge structure cross-section, is the mean value of the cross-section live load effect of the i-th bridge structure cross-section.​​​ According to the formula +1.4 , the standard deviation of the cross-section load response of the first bridge structure cross-section is calculated , wherein, is the standard deviation of the cross-section dead load effect of the first bridge structure cross-section, is the standard deviation of the cross-section stress under the action of the first bridge structure cross-section live load.

6. The method for evaluating dynamic reliability of a bridge structure system according to claim 1, wherein: Step 402, the probability of two failure modes failing simultaneously wherein, , is the correlation coefficient of the monitoring data and the monitoring data .

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